Step function phenomena are widespread in nature. Examples of such phenomena are crystalline phase changes and changes in state (e.g., solid to liquid). For homogeneous materials, such changes are generally discrete.
As a particular example of how of such changes can be utilized in applications, a palladium nanowire hydrogen sensor has been described which operates with a response that is inverse to that typically seen in palladium-based hydrogen sensors, i.e., it realizes a decreased resistance when exposed to hydrogen (F. Favier, E. C. Walter, M. P. Zach, T. Benter, R. M. Penner “Hydrogen Sensors and Switches from Electrodeposited Palladium Mesowire Arrays,” Science, 293, p. 2227-2231, 2001). Such nanowires are electrodeposited from perchloric acid (HClO4) solutions onto an electrically-biased graphite step ledge (presumably, these terraced step ledges produce an enhanced field leading to selective deposition). Once formed, these nanowires are transferred to an insulating glass substrate using a cyanoacrylate film. The diameters of these wires are reportedly as small as 55 nm, and they possess gaps or break-junctions which impart them with high resistance. When hydrogen is introduced, a palladium-hydride (PdHx) forms. At room temperature (25° C.), there is a crystalline phase change from α to β when the concentration of hydrogen in air reaches 2% (15.2 Torr). Associated with this phase change is a corresponding 3.5% increase in the lattice parameter of the metal which leads to a “swelling” of the nanowire, thus bridging the nanogap breakjunctions (nanobreakjunctions) and leading to an overall decrease in the resistance along the length of the nanowire. The resistance change that occurs is between 6 and 8 orders of magnitude (typical devices see 1×10−11 amps in the “off” state, and 1×10−4 amps in the “on” state). This behavior is unique to nanowires possessing such nanogap breakjunctions. Fortunately, for sensor applications, these gaps re-open when the nanowires are removed from the hydrogen-containing environment, and the swollen nanowires revert back to their pre-swollen state.
Such above-described sensors have a number of limitations pertaining both to their use and a methods by which they are made. Perhaps most limiting, is their ability to serve merely as a “on/off” sensor by virtue of their crystalline phase change upon exposure to a threshold hydrogen concentration.
As a result of the foregoing, a method for modulating or smoothing step function phenomena would be quite beneficial, particularly where such smoothing permits such above-described hydrogen sensors to be used as continuous-range sensors.